SOLUTION: Please could you kindly help me solve this question.Kindly show me all the working stages. Thank you very very much for your help.
The question: A company suuplies pins to a cus
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-> SOLUTION: Please could you kindly help me solve this question.Kindly show me all the working stages. Thank you very very much for your help.
The question: A company suuplies pins to a cus
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Question 717080: Please could you kindly help me solve this question.Kindly show me all the working stages. Thank you very very much for your help.
The question: A company suuplies pins to a customer. It uses an automatic lathe to produce the pins. Due to factors such as vibration, temperature and wear and tear, the lengths of the pins are normally distributed with a mean of 25.30 mm and a standard deviation of 0.45 mm. The customer will only buy those pins with lengths in the intervals of 25.00 +/- 0.50mm.
a. What percentage of the pins will be acceptable to the customer?
My final answer is:
Therefore 0.1700 + 0.4616 = 0.6316
= 63.16% of the pins will be acceptable.
Is this correct?
b. In order to improve the percentage accepted, management considers adjusting the population mean and standard deviation of the length of the pins. If the lathe can be adjusted to have any desired mean of the lenghts, what should it be adjusted to? Why?
My answer
To improve the acceptance probability of pins, the required mean should be in
the middle of 24.50 and 25.50 so as to cover maximum area.
Thus the mean should be adjusted to the value 25.00 mm.
Is this correct?
c. Suppose that the mean cannot be adjusted but the standard deviation can be reduced. Calculate the maximum reduction in the standard deviation that would make 85% of the pins acceptable? (Assume the mean to be 25.30mm).
I have no idea!!! Please help
d. The production manager the considers the costs involved. The cost of resetting the machine to adjust the population mean involves engineering costs and the cost of production time lost. The cost of reducing the population standard deviation involves, in addition to these costs, the cost of overhauling the machine and reengineering the process. Assume it costs $150 Xsquared to decrease the standard deviation by (x/40)mm. Find the cost of reducing the standard deviation to the values found in C.
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